In reply to Robert Plummer.

A quick internet search is the best (and easiest) place to start. Once you have a couple of possible candidates, read customer reviews about them on places like Yelp and Google Business Reviews to make sure that they are a reputable company and that their past customers have had positive experiences. From there, you will want to give them a call and make sure that they specialize in Rolex and that they are a service center that you feel comfortable working with for the repair of your watch. Additionally, most service centers will offer a warranty on their work, so this is also something to confirm when you speak to them.
Lastly, it is important to make sure that the service center you choose is using nothing but 100% genuine replacement parts. Even a perfectly performed service will not yield satisfactory results if worn or damaged components are replaced with anything other than genuine components.